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How to Write the Equations of a Circle

With any shape on an "x" and "y" plane, a mathematical equation can be conjured using certain points on a graph. In the case of a circle shape, knowing the coordinates for the center of origin and the radius distance is enough information to write an equation of a circle. Using the standard equation (x - h)^2 + (y - k)^2 = r^2, you can create an equation relating to the circle's size and position on the graph.

Instructions

- 1
  Identify the circle's center coordinates, also known as the "origin." If your circle has a center at (0,0), you will use the equation x^2 + y^2 = r^2 where "r" represents the radius of the circle. If your circle has a center at another point on the graph, you will use the equation (x-h)^2 + (y-k)^2 = r^2 where "h" and "k" represent the coordinates of the circle's center (h,k) and "r' represents the radius.
- 2
  Plot the center coordinates on the graph by finding the "x" and "y" coordinates on the graph. For example, if the center of the circle is two units to the left and five units down, the center of the circle is at coordinates (2, -5).
- 3
  Find the radius of the circle by counting the units outwards from the center of the circle to the boundary of the circle farthest away from the center. The easiest way to measure the radius would be to count either directly up, down, left or right from the center of the circle.
- 4
  Formulate the equation by plugging in the information you have obtained from steps 2 and 3. For example, for a circle whose center coordinates were (2, -5) and has a radius of 3, the equation the circle can be written as:
  
  (x-2)^2 + (y + 5)^2 = (3)^2

Numerology